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   "source": [
    "# Introduction: Logistic Regression\n",
    "\n",
    "The purpose of this notebook is to gain an understanding of the simple method of logistic regression. Logistic regression is generally considered the simplest method of classification, but can still be a powerful and explainable algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:39:59.201883Z",
     "start_time": "2019-03-03T02:39:55.859824Z"
    }
   },
   "outputs": [
    {
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    }
   ],
   "source": [
    "# Standard Data Science Helpers\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy\n",
    "\n",
    "import plotly.plotly as py\n",
    "import plotly.graph_objs as go\n",
    "from plotly.offline import iplot, init_notebook_mode\n",
    "init_notebook_mode(connected=True)\n",
    "\n",
    "import cufflinks as cf\n",
    "cf.set_config_file(world_readable=True, theme=\"pearl\")\n",
    "cf.go_offline(connected=True)\n",
    "\n",
    "# Extra options\n",
    "pd.options.display.max_rows = 10\n",
    "pd.options.display.max_columns = 25\n",
    "# Show all code cells outputs\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = 'all'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:39:59.417304Z",
     "start_time": "2019-03-03T02:39:59.204879Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 32561 entries, 0 to 32560\n",
      "Data columns (total 20 columns):\n",
      "age                                      32561 non-null int64\n",
      "weighting                                32561 non-null int64\n",
      "education_num                            32561 non-null int64\n",
      "hours_per_week_work                      32561 non-null int64\n",
      "target                                   32561 non-null int64\n",
      "female                                   32561 non-null int64\n",
      "capital                                  32561 non-null int64\n",
      "marital_status_ Divorced                 32561 non-null uint8\n",
      "marital_status_ Married-AF-spouse        32561 non-null uint8\n",
      "marital_status_ Married-civ-spouse       32561 non-null uint8\n",
      "marital_status_ Married-spouse-absent    32561 non-null uint8\n",
      "marital_status_ Never-married            32561 non-null uint8\n",
      "marital_status_ Separated                32561 non-null uint8\n",
      "marital_status_ Widowed                  32561 non-null uint8\n",
      "relationship_ Husband                    32561 non-null uint8\n",
      "relationship_ Not-in-family              32561 non-null uint8\n",
      "relationship_ Other-relative             32561 non-null uint8\n",
      "relationship_ Own-child                  32561 non-null uint8\n",
      "relationship_ Unmarried                  32561 non-null uint8\n",
      "relationship_ Wife                       32561 non-null uint8\n",
      "dtypes: int64(7), uint8(13)\n",
      "memory usage: 2.1 MB\n"
     ]
    }
   ],
   "source": [
    "original_data = pd.read_csv('data/adult_income.csv')\n",
    "\n",
    "def process_data(data):\n",
    "    \"\"\"\n",
    "    Process the adult income dataset\n",
    "    \"\"\"\n",
    "    data = data.copy()\n",
    "    # Replace missing values\n",
    "    data = data.replace({' ?': np.nan})\n",
    "    \n",
    "    # Code gender\n",
    "    data['female'] = data['sex'].replace({' Male': 0, ' Female': 1})\n",
    "    # Code target\n",
    "    data['target'] = data['target'].replace({' >50K': 1, ' <=50K': 0})\n",
    "    # Create single column for capital wealth\n",
    "    data['capital'] = data['capital_gain'] - data['capital_loss']\n",
    "    to_drop = ['country', 'education', 'sex', \n",
    "           'capital_gain', 'capital_loss', \n",
    "           'working_class',\n",
    "          'race', 'occupation']\n",
    "    # Remove excess columns\n",
    "    data = data.drop(columns=to_drop)\n",
    "    data = pd.get_dummies(data)\n",
    "    return data\n",
    "\n",
    "data = process_data(original_data)\n",
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:39:59.493103Z",
     "start_time": "2019-03-03T02:39:59.419304Z"
    }
   },
   "outputs": [
    {
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       "weighting                      -0.009463\n",
       "education_num                   0.335154\n",
       "hours_per_week_work             0.229689\n",
       "target                          1.000000\n",
       "                                  ...   \n",
       "relationship_ Not-in-family    -0.188497\n",
       "relationship_ Other-relative   -0.083716\n",
       "relationship_ Own-child        -0.228532\n",
       "relationship_ Unmarried        -0.142857\n",
       "relationship_ Wife              0.123264\n",
       "Name: target, Length: 20, dtype: float64"
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     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "corrs = data.corr()\n",
    "corrs['target']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:40:00.974140Z",
     "start_time": "2019-03-03T02:39:59.496095Z"
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{\"dtick\": 1, \"gridcolor\": \"rgb(0, 0, 0)\", \"side\": \"top\", \"ticks\": \"\"}, \"yaxis\": {\"dtick\": 1, \"ticks\": \"\", \"ticksuffix\": \"  \"}}, {\"showLink\": false, \"linkText\": \"Export to plot.ly\", \"plotlyServerURL\": \"https://plot.ly\"})});</script><script type=\"text/javascript\">window.addEventListener(\"resize\", function(){window._Plotly.Plots.resize(document.getElementById(\"0e928bf5-c7af-4e92-bba8-d9a348e49e99\"));});</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import plotly.figure_factory as ff\n",
    "from plotly.offline import iplot\n",
    "\n",
    "# Correlation Heatmap\n",
    "iplot(ff.create_annotated_heatmap(corrs.iloc[:10, :10].round(3).values, x=list(corrs.iloc[:10, :10].columns), \n",
    "                                  y=list(corrs.iloc[:10, :10].index), annotation_text=corrs.iloc[:10, :10].round(3).values))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:40:03.873386Z",
     "start_time": "2019-03-03T02:40:00.976134Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Done   3 out of   3 | elapsed:    2.3s finished\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LogisticRegressionCV(Cs=10, class_weight=None, cv=3, dual=False,\n",
       "           fit_intercept=True, intercept_scaling=1.0, max_iter=100,\n",
       "           multi_class='ovr', n_jobs=-1, penalty='l2', random_state=42,\n",
       "           refit=True, scoring='roc_auc', solver='lbfgs', tol=0.0001,\n",
       "           verbose=1)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegressionCV\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# Features and target\n",
    "X = data.copy()\n",
    "y = X.pop('target')\n",
    "\n",
    "# Split into training and testing\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=42)\n",
    "\n",
    "# Create the model\n",
    "model = LogisticRegressionCV(Cs=10, cv = 3, scoring='roc_auc', n_jobs=-1, verbose=1, random_state=42)\n",
    "model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:40:03.914278Z",
     "start_time": "2019-03-03T02:40:03.877378Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ROC AUC: 0.5500\n",
      "F1 Score: 0.3103\n",
      "Accuracy: 79.59%\n",
      "Baseline Accuracy: 75.97%\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import f1_score, roc_auc_score\n",
    "\n",
    "def evaluate(model, X_test, y_test):\n",
    "    \"\"\"\n",
    "    Test a model on a few classification metrics.\n",
    "    \"\"\"\n",
    "    # Predictions and probabilities\n",
    "    predictions = model.predict(X_test)\n",
    "    probabilities = model.predict_proba(X_test)[:, 1]\n",
    "    roc_auc = roc_auc_score(y_test, probabilities)\n",
    "    f1_value = f1_score(y_test, predictions)\n",
    "    accuracy = np.mean(predictions == y_test)\n",
    "    \n",
    "    # Get a baseline\n",
    "    base_accuracy = np.mean(y_test == 0)\n",
    "    print(f'ROC AUC: {roc_auc:.4f}')\n",
    "    print(f'F1 Score: {f1_value:.4f}')\n",
    "    print(f'Accuracy: {100 * accuracy:.2f}%')\n",
    "    print(f'Baseline Accuracy: {100 * base_accuracy:.2f}%')\n",
    "    \n",
    "evaluate(model, X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:40:03.968149Z",
     "start_time": "2019-03-03T02:40:03.918267Z"
    }
   },
   "outputs": [],
   "source": [
    "probability = model.predict_proba(X_test)[:, 1]\n",
    "log_odds = model.decision_function(X_test)\n",
    "classes = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:40:04.072854Z",
     "start_time": "2019-03-03T02:40:03.972123Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probability</th>\n",
       "      <th>log_odds</th>\n",
       "      <th>classes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>13025.000000</td>\n",
       "      <td>13025.000000</td>\n",
       "      <td>13025.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.278616</td>\n",
       "      <td>-0.891544</td>\n",
       "      <td>0.055585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.148823</td>\n",
       "      <td>2.021135</td>\n",
       "      <td>0.229128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.002541</td>\n",
       "      <td>-5.972546</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.201376</td>\n",
       "      <td>-1.377718</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.252283</td>\n",
       "      <td>-1.086475</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.317065</td>\n",
       "      <td>-0.767294</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>24.621157</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        probability      log_odds       classes\n",
       "count  13025.000000  13025.000000  13025.000000\n",
       "mean       0.278616     -0.891544      0.055585\n",
       "std        0.148823      2.021135      0.229128\n",
       "min        0.002541     -5.972546      0.000000\n",
       "25%        0.201376     -1.377718      0.000000\n",
       "50%        0.252283     -1.086475      0.000000\n",
       "75%        0.317065     -0.767294      0.000000\n",
       "max        1.000000     24.621157      1.000000"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat = pd.DataFrame(dict(probability=probability, log_odds=log_odds, classes=classes))\n",
    "yhat.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Converting Between Log Odds and Probabilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:40:04.118734Z",
     "start_time": "2019-03-03T02:40:04.077841Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_odds = yhat['log_odds']\n",
    "\n",
    "# Exponentiate the log odds\n",
    "odds_ratio = np.exp(log_odds)\n",
    "\n",
    "# Calculate the probabilitiy\n",
    "probability = odds_ratio / (1 + odds_ratio)\n",
    "\n",
    "# Sanity check\n",
    "np.allclose(probability, yhat['probability'].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualization of Log Odds and Probabilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:40:04.173586Z",
     "start_time": "2019-03-03T02:40:04.122721Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_odds = yhat['log_odds']\n",
    "\n",
    "# Apply sigmoid function by hand\n",
    "probability = 1 / (1 + np.exp(-log_odds))\n",
    "\n",
    "# Check\n",
    "np.allclose(probability, yhat['probability'].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:40:04.243401Z",
     "start_time": "2019-03-03T02:40:04.177574Z"
    }
   },
   "outputs": [],
   "source": [
    "yhat['odds_ratio'] = odds_ratio\n",
    "yhat['classes'] = yhat['classes'].map({0: '< 50K', 1: '>= 50K'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:40:04.962472Z",
     "start_time": "2019-03-03T02:40:04.252377Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "linkText": "Export to plot.ly",
        "plotlyServerURL": "https://plot.ly",
        "showLink": true
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       "data": [
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   "source": [
    "yhat.sample(1000).iplot(x='log_odds', y='probability', \n",
    "           yTitle='Probability', xrange=(-5, 5), xTitle='Log Odds',\n",
    "           title='Probability vs Log Odds', categories='classes')"
   ]
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  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:40:05.181889Z",
     "start_time": "2019-03-03T02:40:04.963469Z"
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   "source": [
    "yhat.sample(1000).iplot(x='log_odds', y='odds_ratio', \n",
    "           yTitle='odds_ratio', xrange=(-2, 4), yrange=(0,15),\n",
    "           title='Odds Ratio vs Log Odds', categories='classes')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:40:05.357417Z",
     "start_time": "2019-03-03T02:40:05.183883Z"
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   "source": [
    "yhat.sample(1000).iplot(x='odds_ratio', y='probability', xTitle='Odds Ratio', yTitle='Probability', \n",
    "                        title='Probability vs Odds Ratio', \n",
    "                        mode='markers', xrange=(0, 10))"
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       "      <th>probability</th>\n",
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       "      <th>12289</th>\n",
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       "      <th>714</th>\n",
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       "       probability  log_odds classes  odds_ratio\n",
       "12289     0.333226 -0.693630   < 50K    0.499759\n",
       "7075      0.321340 -0.747621   < 50K    0.473492\n",
       "714       0.289100 -0.899762   < 50K    0.406667\n",
       "760       0.303536 -0.830516   < 50K    0.435824\n",
       "12278     0.343228 -0.648944   < 50K    0.522598\n",
       "...            ...       ...     ...         ...\n",
       "4207      0.182416 -1.500063   < 50K    0.223116\n",
       "3001      0.305110 -0.823083   < 50K    0.439076\n",
       "7006      0.163736 -1.630690   < 50K    0.195794\n",
       "5065      0.241372 -1.145171   < 50K    0.318170\n",
       "1770      0.211092 -1.318357   < 50K    0.267574\n",
       "\n",
       "[1000 rows x 4 columns]"
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    "yhat.sort_values('probability').sample(1000)"
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          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          ">= 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
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          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
          ">= 50K",
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          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
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          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
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          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
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          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
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          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          ">= 50K",
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          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
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          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
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          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
          "< 50K",
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          "< 50K",
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          "< 50K",
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          "< 50K",
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\"#F5F6F9\", \"font\": {\"color\": \"#4D5663\"}}, \"paper_bgcolor\": \"#F5F6F9\", \"plot_bgcolor\": \"#F5F6F9\", \"title\": {\"text\": \"Odds and Log Odds vs Probability\", \"font\": {\"color\": \"#4D5663\"}}, \"xaxis\": {\"gridcolor\": \"#E1E5ED\", \"showgrid\": true, \"tickfont\": {\"color\": \"#4D5663\"}, \"title\": {\"text\": \"Probability\", \"font\": {\"color\": \"#4D5663\"}}, \"zerolinecolor\": \"#E1E5ED\"}, \"yaxis\": {\"gridcolor\": \"#E1E5ED\", \"range\": [0, 10], \"showgrid\": true, \"tickfont\": {\"color\": \"#4D5663\"}, \"title\": {\"text\": \"Odds\", \"font\": {\"color\": \"#4D5663\"}}, \"zerolinecolor\": \"#E1E5ED\"}}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\", \"plotlyServerURL\": \"https://plot.ly\"})});</script><script type=\"text/javascript\">window.addEventListener(\"resize\", function(){window._Plotly.Plots.resize(document.getElementById(\"707f87f8-049b-44c7-b3e0-349ee3dfedd7\"));});</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "yhat.sort_values('probability').sample(1000).iplot(x='probability', mode='markers',\n",
    "                                                   yrange=(0, 10), xTitle='Probability', yTitle='Odds',\n",
    "                                                   title=\"Odds and Log Odds vs Probability\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:40:06.399645Z",
     "start_time": "2019-03-03T02:40:05.839128Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ROC AUC: 0.8700\n",
      "F1 Score: 0.6188\n",
      "Accuracy: 83.32%\n",
      "Baseline Accuracy: 75.97%\n"
     ]
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "model = RandomForestClassifier()\n",
    "_=model.fit(X_train, y_train)\n",
    "evaluate(model, X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-03T02:43:03.524871Z",
     "start_time": "2019-03-03T02:43:01.158163Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ROC AUC: 0.9052\n",
      "F1 Score: 0.6649\n",
      "Accuracy: 85.53%\n",
      "Baseline Accuracy: 75.97%\n"
     ]
    }
   ],
   "source": [
    "model = RandomForestClassifier(n_estimators=100, max_depth=20, random_state=50)\n",
    "_ = model.fit(X_train, y_train)\n",
    "evaluate(model, X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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